I find the answers here very interesting because, like @jdln, I had always used this to mean to phone someone. If I ever asked someone to drop me a line I was certainly expecting a call.
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Andy FNov 21 '11 at 15:16

To get someone on the line means to establish a telephone connection, and you can say the line dropped if that connection is lost involuntarily, but I've never heard drop a line used to mean contact by telephone.
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FumbleFingersNov 21 '11 at 15:50

1

@FumbleFingers When used as "drop me a line", think of the "line" being drop/tossed in the direction of the person.
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IzkataNov 21 '11 at 18:57

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I can imagine how OP and Andy came to their understanding of the usage - I'm just saying I've never come across it before. Nor have the three people who've posted answers, apparently.
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FumbleFingersNov 21 '11 at 19:11

Sites like this one and this one show that's it's not unheard of. These are both from the first page of Google results for the phrase "drop us a line". I wonder if the confusion lies somewhere between a line of text and a telephone line.
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Andy FNov 21 '11 at 21:07

It's funny how many phrases in language completely lose context with their origins over time. "Drop a call" seems like a different nuance than "drop a line". And there is the action of dropping a line as in the actual telephone cable line being dropped into the ground for installation.

I also interpret "drop me a line" to come from dropping someone a line of rope to reach them (connect with them). By that interpretation, and mode of communication involving any kind of line seems to qualify – a telephone line, a line of text, or even a pickup line in a bar (which has the added irony of dropping vs. picking up) :)

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chosterJul 31 '14 at 17:46